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NCERT Class 12 Physics Chapter 8 Notes Electromagnetic Waves - Download PDF

NCERT Class 12 Physics Chapter 8 Notes Electromagnetic Waves - Download PDF

Edited By Vishal kumar | Updated on Feb 02, 2024 05:16 PM IST

Class 12 Physics Chapter 8, which focuses on Electromagnetic Waves, is a significant part of the NCERT curriculum. These meticulously crafted class 12 physics chapter 8 notes cover important topics like Maxwell's Equations, energy density, and the transverse nature of electromagnetic waves. They provide comprehensive coverage of the chapter's major themes and are essential resources for students preparing for the CBSE Exam and other competitive tests.

These Electromagnetic Waves class 12 notes, available as PDF downloads, provide students with a convenient way to improve their understanding of electromagnetic phenomena. These ch 8 physics class 12 notes delve into fundamental concepts required for academic success, such as the relationship between vector E and vector B and the electromagnetic spectrum. With a focus on clarity and conciseness, they provide students with the knowledge and skills required to excel not only in exams but also in broader academic endeavours.

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NCERT Class 12 Chapter 8 Electromagnetic Waves Notes-

Maxwell’s Equations

Maxwell put together the basic laws of electricity and magnetism is that, Gauss’ law of electricity, Gauss’ law of magnetism, Faraday’s law of electromagnetic induction, and Ampere- Maxwell’s Circuital law in the form of four fundamental equations, known as Maxwell’s equations.

On the basis of these equations, Maxwell anticipated the existence of electromagnetic waves.

  1. Gauss’ law of electricity:- It states that the electric flux through any closed surface is equal to the 1/?₀ times the net charge enclosed by the surface.


This equation is called Maxwell’s first equation. This equation is true for both moving and stationary charges.

  1. Gauss’s law of magnetism:- It states that the magnetic flux through any closed surface is zero.

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This equation is called Maxwell’s second equation. It signifies that free magnetic poles do not exist. This equation also signifies that magnetic lines of force cannot start from a point nor end at a point, that is they are closed curves.

  1. Faraday’s laws of Electromagnetic induction:- It asserts that the negative rate of change of magnetic flux across a circuit is equal to the induced emf set up in the circuit.


Since emf can be defined as the line integral of the electric field, the above relation can be expressed as


The line integral of the electric field along a closed channel is therefore equal to the rate of change of magnetic flux through the surface bounded by that closed path, according to the law.

This equation is called Maxwell's third equation. It signifies that the electric field is produced by a changing magnetic field.

  1. Ampere-Maxwell’s Circuital law:- It states that the line integral of the magnetic field along a closed is equal to μ₀ times the total current linked with the surface bounded by that closed path.




This equation is known as Maxwell’s fourth equation. It signifies that a conduction current, as well as a changing electric field, produces a magnetic field.

Electromagnetic Waves

From the Maxwell third equation is that a changing magnetic field produces an electric field whereas Maxwell’s fourth equation is, a changing electric field produces a magnetic field. It means that change in either field produces the other field. Maxwell worked out from his quotations that variation in electric and magnetic fields would lead to a wave consisting of fluctuating electric and magnetic fields perpendicular to each other and also perpendicular to the propagation of the wave. Such waves can actually propagate in space without any material medium called electromagnetic waves.

A graphical representation of electromagnetic waves is shown in fig. In this electric field vector E and the magnetic field, vectors B are vibrating along the Y- and Z- directions respectively and the wave is propagating along the X-direction. Both vector E and vector B are varied with time and space and have the same frequency. Some examples of electromagnetic waves are radio waves, microwaves, infrared rays, ultraviolet rays, X-rays, and ?-rays.

Relation Between Magnitudes of Vector E and Vector B in Free Space

Let a sinusoidal electromagnetic wave is propagating in free space along with the positive directions o the X-axis with wave no. k and angular frequency ?. Then, the magnitudes of vector E and vector B acting along Y- and Z-axis respectively, vary with x and t and can be written as

{"code":"\\begin{lalign*}\n&{E\\,=\\,E_{0}\\sin\\left(\\omega t\\,-\\,kx\\right)\\,\\,\\,\\,\\,\\,\\,\\,.....\\left(i\\right)}\\\\\n&{B\\,=\\,B_{0}\\sin\\left(\\omega t-\\,kx\\right)\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,......\\left(ii\\right)}\t\n\\end{lalign*}","font":{"color":"#000000","size":11,"family":"Arial"},"backgroundColorModified":false,"backgroundColor":"#ffffff","id":"13-0","type":"lalign*","aid":null,"ts":1637058537024,"cs":"s5GK50K+pmCsp4nSRLNklQ==","size":{"width":261,"height":38}}

Where E₀ and B₀ are the maximum values of E and B respectively.

{"aid":null,"backgroundColorModified":false,"backgroundColor":"#ffffff","type":"$$","code":"$$k\\,=\\,\\frac{2\\pi}{\\lambda}\\,,\\,\\omega=\\,2\\pi v$$","font":{"size":11,"color":"#000000","family":"Arial"},"id":"14","ts":1637058684325,"cs":"sxGxVjypAkA5jtUTuipP8w==","size":{"width":138,"height":34}}

Here λ is wavelength and v is the frequency of the wave.

{"id":"15","backgroundColor":"#ffffff","font":{"color":"#000000","size":11,"family":"Arial"},"aid":null,"backgroundColorModified":false,"type":"$$","code":"$$\\therefore \\frac{\\omega}{k}\\,=\\,\\frac{2\\pi v}{2\\pi/\\lambda}\\,=\\,v\\lambda=\\,c$$","ts":1637058827161,"cs":"wafZlG/XiuNjRKTNMI7xnQ==","size":{"width":186,"height":38}}

c is the speed of the electromagnetic wave which is the speed of light in free space. From eqn (i),

{"id":"16-0","backgroundColor":"#ffffff","code":"$$\\frac{\\partial E}{\\partial x}\\,=\\,-\\,kx\\cos\\left(\\omega t\\,-\\,kx\\right)$$","aid":null,"font":{"family":"Arial","size":11,"color":"#000000"},"backgroundColorModified":false,"type":"$$","ts":1637059250904,"cs":"XFMnJ4sXZGYBx0N92k78fw==","size":{"width":201,"height":36}}

From eqn (ii),

{"id":"17","code":"$$\\frac{\\partial B}{\\partial t}\\,=\\,\\omega B_{0}\\cos \\left(\\omega t\\,-\\,kx\\right)$$","backgroundColor":"#ffffff","backgroundColorModified":false,"type":"$$","aid":null,"font":{"family":"Arial","size":11,"color":"#000000"},"ts":1637059334418,"cs":"a8xUO/JGkUQR2jevqJv78g==","size":{"width":189,"height":36}}

Putting these values in this relation

\frac{\partial \vec E}{\partial x}=-\frac{\partial \vec B}{\partial t}

, we get

{"aid":null,"backgroundColorModified":false,"font":{"color":"#000000","family":"Arial","size":11},"backgroundColor":"#ffffff","type":"$$","id":"16-1","code":"$$\\,kx\\cos\\left(\\omega t\\,-\\,kx\\right)\\,=\\,\\omega B_{0}\\cos\\left(\\omega t\\,-\\,kx\\right)$$","ts":1637059846805,"cs":"a4bndvRSd/PX8F5dNNsXlQ==","size":{"width":284,"height":16}}


Since E and B are in the same phase.


At any point in space. Thus, the ratio of the magnitude of electric field and magnetic field equals the speed of light in free space.

Energy Density in Electromagnetic Waves

The energy density in an electric field E in a vacuum is ϵ0E2/2, and that in a magnetic field B is B2/2μ0. Thus, the energy density is associated with an electromagnetic wave is


An electromagnetic wave propagating along the X-axis and the magnitude of vector E and vector B, acting along the Y- and Z- axis respectively can be written as

{"backgroundColor":"#ffffff","type":"lalign*","backgroundColorModified":false,"font":{"color":"#000000","family":"Arial","size":11},"aid":null,"id":"13-1","code":"\\begin{lalign*}\n&{E\\,=\\,E_{0}\\sin\\left(\\omega t\\,-\\,kx\\right)\\,\\,\\,\\,and\\,B\\,=\\,B_{0}\\sin\\left(\\omega t-\\,kx\\right)\\,\\,\\,}\\\\\n&{\\,\\,}\t\n\\end{lalign*}","ts":1637060990075,"cs":"RhMQu61NuJyneLMLPWyJow==","size":{"width":365,"height":16}}

Where E₀ and B₀ are the maximum values of E and B respectively. Putting these values in eqn (i), we get

{"code":"$$u\\,=\\,\\frac{1}{2}\\epsilon_{0}E_{0}^{2}\\sin^{2}\\left(\\omega t\\,-\\,kx\\right)\\,+\\,\\frac{1}{2}\\frac{B_{0}^{2}}{\\mu_{0}}\\,\\sin^{2}\\left(\\omega t\\,-\\,kx\\right)\\,$$","backgroundColorModified":null,"backgroundColor":"#ffffff","aid":null,"id":"28","font":{"size":11,"color":"#000000","family":"Arial"},"type":"$$","ts":1637061227396,"cs":"f7bJ6Rect2z6RXflci+6vg==","size":{"width":380,"height":42}}

The time average of sin² over any whole number of cycles is ½. Therefore the average energy density of an e.m. wave is


Here ϵ0E2/2 is the average kinetic energy density ue and B2/2μ0 is the average magnetic density um.

Important Characteristics of Electromagnetic Waves

  1. The electromagnetic waves are produced by accelerated charge.

  2. In free space, these waves travel with the speed of light.

  3. No medium is required for the propagation of Electromagnetic waves.

  4. The electric and magnetic fields have perpendicular variations in their direction of variation.

  5. The electromagnetic waves are transverse in nature.

  6. The variations in the electric and magnetic fields occur simultaneously and the field acquires their maximum values E₀ and B₀ at the same place and same time.

  7. In free space, the magnitudes of the electric and magnetic fields in electromagnetic waves are related by E/B = c.

  8. Electromagnetic waves, being uncharged, are not deflected by electric and magnetic fields.

Electromagnetic Spectrum

In the visible spectrum, the sunlight extends in wavelength from 4 x 10⁻⁷m in the violet region to 8 x 10⁻⁷m in the red region. Some parts are not visible from the eyes so, they are called ‘invisible spectra’ of the sun. The part of smaller wavelengths below violet is called the ‘ultraviolet spectrum’ and that of longer wavelengths above red is called the ‘infrared spectrum’.

Later on, were discovered X-rays and gamma rays. These were also found to travel in free space with the speed of light, and thus of electromagnetic nature. The range of wavelength of all these radiations is very large and on this basis, they have been given in order. This order is called the “electromagnetic spectrum”.

The wavelength-ranges. Frequency ranges, methods of production, properties, and uses of the various regions of the electromagnetic spectrum are summarised

  1. Gamma Rays

Wavelength range: 1 x 10¹⁴ to 1 x 10⁻¹⁰m

Frequency range: 3 x 10²² to 3 x 10¹⁸Hz

Production: By transition of atomic nuclei and decay of certain elementary particles.

Properties: Chemical reaction on photographic plates, fluorescence, ionization, diffraction, highly-penetrating, chargeless, harmful to the human body

Uses: Provide information about the structure of atomic nuclei.

  1. X- rays

Wavelength range: 1 x 10⁻¹¹ to 3 x 10⁻⁸m

Frequency range: 3 x 10¹⁹ to 1 x 10¹⁶Hz

Production: By sudden deceleration of high-speed electrons at a high-atomic number target, and also by the electronic transition among the innermost orbits of atoms.

Properties: All properties of gamma rays but less penetrating.

Uses: For studying structures of inner atomic electron shells and crystals, For detection of fractures, diseased organs, formation of bones and stones, for detecting faults, cracks, flaws, and holes in metal products and to cure untraceable skin diseases, in cancer-like diseases.

  1. Ultraviolet- Rays

Wavelength range: 1 x 10⁻⁸ to 3 x 10⁻⁸m

Frequency range: 3 x 10¹⁶ to 1 x 10¹⁴Hz

Production: By sun, arc, vacuum spark, and ionized gases.

Properties: All properties of gamma rays but less penetrating produce a photoelectric effect, absorbed by atmospheric ozone, harmful to the human body.

Uses: In the detection of invisible writing, forged documents, fingerprints and to preserve foodstuffs, to destroy bacteria and for sterilizing the surgical instruments, in burglars alarm, in studying molecular structure.

  1. Visible Light

Wavelength range: 1 x 10⁻⁷ to 1 x 10⁻⁷m

Frequency range: 7 x 10¹⁴ to 4 x 10¹⁴Hz

Production: Radiated by excited atoms in gases and incandescent bodies.

Properties: Reflection, refraction, interference, diffraction, polarisation, photo-electric effect, photographic effect, photographic action, and sensation of sight.

Uses: Reveals the structure of molecules and arrangement of electrons in external shells of atoms.

5. Infrared Radiation

Wavelength range: 8 x 10⁻⁷ to 5 x 10⁻³m

Frequency range: 4x 10¹⁴ to 6 x 10¹⁰ Hz

Production: From hot bodies, and by rotational and vibrational transitions in molecules.

properties: Heating effect on thermopile and bolometer, reflection, refraction, diffraction, penetrating through fog.

Uses: For providing electrical energy to satellites by means of solar cells, for producing dehydrated fruits, for treating muscular strain, in solar water heaters and cookers, for weather forecasting through infrared photography, in greenhouses to keep the plants warm and in warfare to look through the haze, fog, or mist.

  1. Microwave

Wavelength range: 1 x 10⁻³ to 3 x 10⁻¹m

Frequency range: 3 x 10¹¹ to 1 x 10⁹ Hz

Production: By oscillating currents in special vacuum tubes, and by electromagnetic oscillators in electric circuits.

Properties: Reflection, polarisation.

Uses: In radar for aircraft navigation, long-distance wireless communication via satellites and in microwave ovens.

  1. Radio waves

Wavelength range: 1 x 10⁻¹ to 1 x 10⁴m

Frequency range: 3 x 10⁹ to 3 x 10⁴ Hz

Production: By oscillating electric circuits.

Properties: Reflection and diffraction.

Uses: In radio and T.V. communication systems. Cellular phones use radio waves to transmit voice communication in the ultra-high frequency (UHF) band

  1. Long Waves

Wavelength range: 5 x 10⁶ to 6 x 10⁶m

Frequency range: 60 to 50 Hz

Production: Weak radiation from a.c. circuits.

Significance of NCERT Class 12 Physics Chapter 8 Notes

Comprehensive Revision: The NCERT electromagnetic waves class 12 notes on electromagnetic waves provide a structured approach to revising the chapter by providing an overview of the major topics covered.

CBSE Exam Preparation: These ch 8 physics class 12 notes are invaluable for CBSE Class 12 Physics exams, covering key concepts and topics from the NCERT syllabus.

Preparation for Competitive Exams: In addition to CBSE exams, these class 12 physics chapter 8 notes can help you prepare for VITEEE, BITSAT, JEE MAIN, NEET and other competitive exams. They help to reinforce the understanding and application of electromagnetic wave principles.

Offline Preparation Convenience: These CBSE class 12 physics ch 8 notes, which are available as PDF downloads, allow students to study whenever and wherever they want, according to their schedule.

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Frequently Asked Question (FAQs)

1. What is the relation between the magnitudes of E and B in free space ?

From NCERT Class 12 Physics chapter 8 notes

The relation between the magnitudes of E and B in free space is E/B=C.

2. Write five important characteristics of Electromagnetic Waves.

i. The electromagnetic waves are produced by accelerated charge.

ii. These waves travel in free space at the speed of light.

iii. These waves do not require any material medium for propagation.

iv. The direction of variation of the electric and magnetic fields are perpendicular to each other.

v. The electromagnetic waves are transverse in nature. 

3. What is the wavelength range of Gamma and X-rays?

According to Class 12 Physics chapter 8 notes and NCERT notes for class 12 physics chapter 8:

The wavelength range of Gamma rays is 1 x 10¹⁴ to 1 x 10⁻¹⁰m and the wavelength range of X-rays is 1 x 10⁻¹¹ to 3 x 10⁻⁸m.

4. What are the number of rays in the electromagnetic spectrum?

As given by  Class 12 Physics chapter 8 notes  and class 12 Electromagnetic waves notes, the number of rays in electromagnetics are

  • Gamma Rays

  • X-rays

  • Ultraviolet-rays     

  • Visible Light

  • Infrared Radiation

  • Microwave

  • Radio waves

  • Long Waves

These topics can also be downloaded from Electromagnetic waves Class 12 notes pdf download.


Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg


An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)


Option 2)

\; K\;

Option 3)


Option 4)


In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)


Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)


Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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